An algebraic approach to Quantum Mechanics: a precursor for Quantum Computing

The main idea in Quantum Computing is to use Quantum Mechanical Phenomena that have no classical counterpart to use for computational purposes. Now Quantum Computing is intrinsically linear algebraic. So to make the quantum problem under consideration amenable to quantum computing some algebraic approach must be adopted. In this work, we have looked at the spin algebra of helium triplet states and calculated the matrix elements for spin spin and spin orbit corrections in the Hamiltonian using the concepts of Tensor Products. We found good agrrement with the previous results obtained by conventional quantum mechanics. Our results based on the spin algebra can be dissiminated for constructing the quantum gates and quantum algorithm as a future direction of the present work.